Topicalization or fronting: constituent appears at the beginning, separated with a comma (or prosodical equivalent, when speaking). Examples:

She ate spaghetti with meatballs / Spaghetti with meatballs, she ate.

She ate spaghetti with chopsticks / *Spaghetti with chopsticks, she ate. In this case, the test does not work because spaghetti with chopsticks is not a constituent (with chopsticks modifies the verb, not the noun).

Clefting: re-build the sentence beginning with It is / it was followed by the constituent and a relative pronoun. Examples:

It was spaghetti with meatballs that she ate.

*It was spaghetti with chopsticks that she ate. Again, the test fails because spaghetti with chopsticks is not a constituent.

It is that big furry cat who is sleeping.

Substitution

By pronoun, proper noun, or other single-word constituent. Examples:

That big furry cat is sleeping / Lola is sleeping / She is sleeping.

Bruna went to the fair / Bruna went there.

By interrogative pronoun (aka WH-word) in partial questions (note that this test involves both rearrangement and substitution). Examples:

That big furry cat is sleeping / Who is sleeping?

Bruna went to the fair / Where did Bruna go?

When a constituent is substitued by a WH-word in a partial question, the constituent is the natural answer to the partial question:

Who is sleeping? Bruna.

Where did Bruna go? To the fair.

By nothing (so, better name for this test: omission). Watch out! It only works for constituents that are syntactically optional (that is, adjuncts rather than complements). Use with care. Examples:

She ate spaghetti with chopsticks / She ate spaghetti.

That big furry cat is sleeping / *Is sleeping. Note: Even if that big furry cat is a constituent, the test fails because subjects are compulsory. So, you should always apply more than one test to double-check conclusions.